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根据数据集绘制高斯钟形曲线？

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根据数据集绘制高斯钟形曲线？

我想绘制钟形曲线来显示数据围绕平均值的分布，具有一到两个标准差。可能的话，比较两个数据集。

我有来自@Stefan Pinnow 的以下代码

% here are your data, just multiplied by 10^9
\begin{filecontents}{data.txt}
    2.9954
    3.1314
    3.1155
    3.094
    2.8861
    3.0875
    2.9685
    3.0532
    2.9003
    3.0931
\end{filecontents}
\documentclass[border=2pt]{standalone}
\usepackage{pgfplots}
    \pgfplotsset{
        % use at least this `compat' level so there is no need to prefix
        % coordinates with "axis cs:"
        compat=1.11,
        %
        /pgf/declare function={
            % `mu' and `sigma' where calculated in Excel using above data
            mu=3.03250;
            sigma=0.0894182;
            % declare gaussian function
            gauss(\x)=1/(sigma*sqrt(2*pi))*exp(-((\x-mu)^2)/(2*sigma^2));
            % precalculate some values
            yA=gauss(mu-2*sigma);
            yB=gauss(mu-sigma);
            % constant to simply change calculating `domain' and x axis limits
            C=2.5;
        },
    }
\begin{document}
    \begin{tikzpicture}
        \begin{axis}[
            % set axis limits and `domain'
            xmin=mu-C*sigma,
            xmax=mu+C*sigma,
            ymin=0,
            domain=mu-C*sigma:mu+C*sigma,
            % -----------------------------------------------------------------
            % nothing changed here
            samples=100,
            axis lines*=left,
            xlabel=$x$,
            every axis x label/.style={
                at=(current axis.right of origin),
                anchor=west,
            },
            height=5cm,
            width=11cm,
            xtick=\empty,
            ytick=\empty,
            axis on top,
            hide y axis,
            % -----------------------------------------------------------------
            % use ticks just at the coordinates of the first `\addplot' ...
            xtick=data,
            % and show the below labels for these ticks
            xticklabels={
                $\mu - 2\sigma$,
                $\mu - \sigma$,
                $\mu$
            },
        ]

        % just a dummy plot used for the `xticklabels'
            \addplot [draw=none,fill=none] coordinates {
                (mu-2*sigma,0)
                (mu-sigma,0)
                (mu,0)
            };
        % plot the data point and the corresponding gauss curve
            \addplot [only marks,cyan]
                table [x index=0,y expr=0] {data.txt};
            \addplot [very thick,cyan!50!black] {gauss(x)};

        % add some lines and labels
            % draw vertical lines
            \draw [gray]
                (mu-2*sigma,0) -- coordinate (A left)  (mu-2*sigma,yA)
                (mu+2*sigma,0) -- coordinate (A right) (mu+2*sigma,yA);
            \draw [gray]
                (mu-sigma,0)   -- coordinate (B left)  (mu-sigma,yB)
                (mu+sigma,0)   -- coordinate (B right) (mu+sigma,yB);
            % draw labels
            \draw [latex-latex]
                (A left) -- node [fill=white] {$0.954$} (A right);
            \draw [latex-latex]
                (B left) -- node [fill=white] {$0.683$} (B right);

        \end{axis}
    \end{tikzpicture}
\end{document}

该图表不符合我的数据！

我的数据是：

\begin{filecontents}{data.txt}
    2.132687
    2.634472
    2.697368
    2.917756
    2.582803
    2.32906
    2.009636
    2.483408
    1.778771
    2.46634
\end{filecontents}

mu=2.403;
sigma=0.327;

答案1

我想现在我已经了解了你的“问题”。

在你的问题代码中给出了 x相对的到 μ 和 σ。y 范围根本没有指定，因此ymax是从计算值中选择的。但给定了，因此，无论选择 μ 和 σ 的值如何，曲线看起来都一样。如果您只是设置一个固定值，然后更改 μ 和 σ 的值，height您会立即看到计算值确实发生了变化。ymax

为了证明我在一个环境中绘制了两条曲线axis，只对代码做了微小的改动以解释 μ 和 σ 值的变化。

% used PGFPlots v1.17
% here are your data, just multiplied by 10^9
\begin{filecontents}{data1.txt}
    2.9954
    3.1314
    3.1155
    3.094
    2.8861
    3.0875
    2.9685
    3.0532
    2.9003
    3.0931
\end{filecontents}
\begin{filecontents}{data2.txt}
    2.132687
    2.634472
    2.697368
    2.917756
    2.582803
    2.32906
    2.009636
    2.483408
    1.778771
    2.46634
\end{filecontents}
\documentclass[border=2pt]{standalone}
\usepackage{pgfplots}
    \pgfplotsset{
        % use at least this `compat' level so there is no need to prefix
        % coordinates with "axis cs:"
        compat=1.11,
        %
        /pgf/declare function={
            % `mu' and `sigma' where calculated in Excel using above data
            mu1=3.03250;
            sigma1=0.0894182;
            mu2=2.403;
            sigma2=0.327;
            % declare gaussian function
            gauss(\x,\mu,\sigma)=1/(\sigma*sqrt(2*pi))*exp(-((\x-\mu)^2)/(2*\sigma^2));
            % precalculate some values
            yA1=gauss(mu1-2*sigma1,mu1,sigma1);
            yB1=gauss(mu1-sigma1,mu1,sigma1);
            % constant to simply change calculating `domain' and x axis limits
            C=2.5;
            %
            xmin=min(mu1-C*sigma1,mu2-C*sigma2);
            xmax=max(mu1+C*sigma1,mu2+C*sigma2);
        },
    }
\begin{document}
    \begin{tikzpicture}
        \begin{axis}[
            % set axis limits and `domain'
            xmin=xmin,
            xmax=xmax,
            ymin=0,
            % -----------------------------------------------------------------
            % nothing changed here
            samples=100,
            axis lines*=left,
            xlabel=$x$,
            every axis x label/.style={
                at=(current axis.right of origin),
                anchor=west,
            },
            height=5cm,
            width=11cm,
            xtick=\empty,
            ytick=\empty,
            axis on top,
            hide y axis,
            % -----------------------------------------------------------------
            % use ticks just at the coordinates of the first `\addplot' ...
            xtick=data,
            % and show the below labels for these ticks
            xticklabels={
                $\mu - 2\sigma$,
                $\mu - \sigma$,
                $\mu$
            },
            smooth,
        ]

        % just a dummy plot used for the `xticklabels'
            \addplot [draw=none,fill=none] coordinates {
                (mu1-2*sigma1,0)
                (mu1-sigma1,0)
                (mu1,0)
            };
        % plot the data point and the corresponding gauss curve
            \addplot [only marks,cyan]
                table [x index=0,y expr=0] {data1.txt};
            \addplot [very thick,cyan!50!black,domain=mu1-C*sigma1:mu1+C*sigma1]
                {gauss(x,mu1,sigma1)};

        % plot the data point and the corresponding gauss curve
            \addplot [only marks,orange]
                table [x index=0,y expr=0] {data2.txt};
            \addplot [very thick,orange!75!black,domain=mu2-C*sigma2:mu2+C*sigma2]
                {gauss(x,mu2,sigma2)};

        % add some lines and labels
            % draw vertical lines
            \draw [gray]
                (mu1-2*sigma1,0) -- coordinate (A left)  (mu1-2*sigma1,yA1)
                (mu1+2*sigma1,0) -- coordinate (A right) (mu1+2*sigma1,yA1);
            \draw [gray]
                (mu1-sigma1,0)   -- coordinate (B left)  (mu1-sigma1,yB1)
                (mu1+sigma1,0)   -- coordinate (B right) (mu1+sigma1,yB1);
            % draw labels
            \draw [latex-latex]
                (A left) -- node [fill=white] {$0.954$} (A right);
            \draw [latex-latex]
                (B left) -- node [fill=white] {$0.683$} (B right);

        \end{axis}
    \end{tikzpicture}
\end{document}

该图显示了上述代码的结果

答案2

不知何故，这个代码有效！

% here are your data, just multiplied by 10^9
\begin{filecontents}{data1.txt}
    2.132687
    2.634472
    2.697368
    2.917756
    2.582803
    2.32906
    2.009636
    2.483408
    1.778771
    2.46634
\end{filecontents}
\begin{filecontents}{data.txt}
    2.065643
    2.031713
    2.055865
    2.365157
    2.227517
    2.008509
    2.790536
    2.167367
    2.269939
    2.065643
\end{filecontents}
\documentclass[border=2pt]{standalone}
\usepackage{pgfplots}
    \pgfplotsset{
        % use at least this `compat' level so there is no need to prefix
        % coordinates with "axis cs:"
        compat=1.11,
        %
        /pgf/declare function={
            % `mu' and `sigma' where calculated in Excel using above data
            mu=2.205;
            sigma=0.234;
            % declare gaussian function
            gauss(\x)=1/(sigma*sqrt(2*pi))*exp(-((\x-mu)^2)/(2*sigma^2));
            % precalculate some values
            yA=gauss(mu-2*sigma);
            yB=gauss(mu-sigma);
            % constant to simply change calculating `domain' and x axis limits
            C=4
            ;
        },
    }
\begin{document}
    \begin{tikzpicture}
        \begin{axis}[
            % set axis limits and `domain'
            xmin=mu-C*sigma,
            xmax=mu+C*sigma,
            ymin=0,
            domain=mu-C*sigma:mu+C*sigma,
            % -----------------------------------------------------------------
            % nothing changed here
            samples=100,
            axis lines*=left,
            xlabel=$x$,
            every axis x label/.style={
                at=(current axis.right of origin),
                anchor=west,
            },
            height=5cm,
            width=11cm,
            xtick=\empty,
            ytick=\empty,
            axis on top,
            hide y axis,
            % -----------------------------------------------------------------
            % use ticks just at the coordinates of the first `\addplot' ...
            xtick=data,
            % and show the below labels for these ticks
            xticklabels={
                $\mu - 2\sigma$,
                $\mu - \sigma$,
                $\mu$,
                $\mu + \sigma$,
                $\mu + 2\sigma$
            },
        ]

        % just a dummy plot used for the `xticklabels'
            \addplot [draw=none,fill=none] coordinates {
                (mu-2*sigma,0)
                (mu-sigma,0)
                (mu,0)
                (mu+sigma,0)
                (mu+2*sigma,0)
            };
        % plot the data point and the corresponding gauss curve
            \addplot [only marks,blue]
                table [x index=0,y expr=0] {data.txt};
            \addplot [very thick,red!50!black] {gauss(x)};

        % add some lines and labels
            % draw vertical lines
            \draw [gray]
                (mu-2*sigma,0) -- coordinate (A left)  (mu-2*sigma,yA)
                (mu+2*sigma,0) -- coordinate (A right) (mu+2*sigma,yA);
            \draw [gray]
                (mu-sigma,0)   -- coordinate (B left)  (mu-sigma,yB)
                (mu+sigma,0)   -- coordinate (B right) (mu+sigma,yB);
            % draw labels
            \draw [latex-latex]
                (A left) -- node [fill=white] {$95 \%$} (A right);
            \draw [latex-latex]
                (B left) -- node [fill=white] {$68 \%$} (B right);

        \end{axis}
    \end{tikzpicture}
\end{document}

输出： 在此处输入图片描述

更新 1：

此代码可适应数据集。我还在同一张图中绘制了三张图来显示差异。但是，正确显示传奇仍然存在问题。\亩价值观体现为剧情，所以传奇就当是剧情吧！

% used PGFPlots v1.17
% here are your data, just multiplied by 10^9
% TEE
\begin{filecontents}{data1.txt}
    2.132687
    2.634472
    2.697368
    2.917756
    2.582803
    2.32906
    2.009636
    2.483408
    1.778771
    2.46634
\end{filecontents}
% ICE
\begin{filecontents}{data2.txt}
    2.065643
    2.031713
    2.055865
    2.365157
    2.227517
    2.008509
    2.790536
    2.167367
    2.269939
    2.065643
\end{filecontents}

% L742
\begin{filecontents}{data3.txt}
    1.67097
    1.65911
    2.96315
    2.46577
    1.61159
    1.46357
    1.59512
    1.87797
    2.37143
    1.16881
\end{filecontents}
\documentclass[border=2pt]{standalone}
\usepackage{pgfplots}
    \pgfplotsset{
        % use at least this `compat' level so there is no need to prefix
        % coordinates with "axis cs:"
        compat=1.11,
        %
        /pgf/declare function={
            % `mu' and `sigma' where calculated in Excel using above data
            mu1=2.40;
            sigma1=0.33;
            mu2=2.2;
            sigma2=0.22;
            mu3=1.88;
            sigma3=0.52;
            % declare gaussian function
            gauss(\x,\mu,\sigma)=1/(\sigma*sqrt(2*pi))*exp(-((\x-\mu)^2)/(2*\sigma^2));
            % precalculate some values
            yA1=gauss(mu1-2*sigma1,mu1,sigma1);
            yB1=gauss(mu1-sigma1,mu1,sigma1);
            yA2=gauss(mu2-2*sigma2,mu2,sigma2);
            yB2=gauss(mu2-sigma2,mu2,sigma2);
            yA3=gauss(mu3-2*sigma3,mu3,sigma3);
            yB3=gauss(mu3-sigma3,mu3,sigma3);
            % constant to simply change calculating `domain' and x axis limits
            C=2.5;
            %
            xmin=min(mu1-C*sigma1,mu2-C*sigma2,mu3-C*sigma3);
            xmax=max(mu1+C*sigma1,mu2+C*sigma2,mu3+C*sigma3);
        },
    }
\begin{document}
    \begin{tikzpicture}
        \begin{axis}[
            legend pos=north west,
            % set axis limits and `domain'
            xmin=xmin,
            xmax=xmax,
            ymin=0,
            % -----------------------------------------------------------------
            % nothing changed here
            samples=100,
            axis lines*=left,
            xlabel=\tiny{$Error$},
            every axis x label/.style={
                at=(current axis.right of origin),
                anchor=west,
            },
            height=5cm,
            width=11cm,
            xtick=\empty,
            ytick=\empty,
            axis on top,
            hide y axis,
            % -----------------------------------------------------------------
            % use ticks just at the coordinates of the first `\addplot' ...
            xtick=data,
            % and show the below labels for these ticks
            xticklabels={
                $\mu_{1}$,
                $\mu_{2}$,
                $\mu_{3}$
            },
            smooth,
        ]

        % just a dummy plot used for the `xticklabels'
            \addplot [draw=none] coordinates {
                (mu1,0)
                (mu2,0)
                (mu3,0)
            };
          \addlegendentry[draw = none]{\tiny{$\mu_{1}=2.40$, $\mu_{2}=2.2$, $\mu_{3}=1.88$}}
        % plot the data point and the corresponding gauss curve TEE
            \addplot [very thick,blue,domain=mu1-C*sigma1:mu1+C*sigma1]
                {gauss(x,mu1,sigma1)};
            \addlegendentry{\footnotesize{TEE}}
            
        % plot the data point and the corresponding gauss curve ICE
            \addplot [very thick,red,domain=mu2-C*sigma2:mu2+C*sigma2]
                {gauss(x,mu2,sigma2)};
            \addlegendentry{\footnotesize{AcuNav (ICE)}}   
            
         % plot the data point and the corresponding gauss curve 742
            \addplot [very thick,green,domain=mu3-C*sigma3:mu3+C*sigma3]
                {gauss(x,mu3,sigma3)};
            \addlegendentry{\footnotesize{L742}}
        % add some lines and labels
           % draw vertical lines
            %TEE
            \draw [blue,very thick,fill=blue]
                (mu1,0) -- coordinate (A left)  (mu1,yA1);
            %ICE
            \draw [red,very thick,fill=red]
                (mu2,0) -- coordinate (A left)  (mu2,yA2);
            %L742
            \draw [fill=green,green,very thick]
                (mu3,0) -- coordinate (A left)  (mu3,yA3);
               
               
            
            % Plot the dots
            % TEE
            \addplot [only marks,blue]
                table [x index=0,y expr=0] {data1.txt};
            % ICE
            \addplot [only marks,red]
                table [x index=0,y expr=0] {data2.txt};
            % 742
            \addplot [only marks,green]
                table [x index=0,y expr=0] {data3.txt};
        \end{axis}
    \end{tikzpicture}
\end{document}

在此处输入图片描述

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